If J, K, L, M, and N and positive integers in ascending order, what is

IMO ans is Option E

Statement 1 says L>3
Statement 2 says L <7

Combining both we get L is between 3 and 7 hence L can be 4, 5 ,6 .
Thus not sufficient because of multiple values

Statement 1 states L is more than 3
Statement 2 states L is less than 7

Combining both we will get L is between 3 and 7 hence L can be between 4 to 6 inclusive .
Thus not sufficient because L could be 4, 5, or 6.

Hence answer is Option E­

Given: J, K, L, M, and N are positive integers in ascending order

Target question: What is the value of L?

Statement 1: The value of K is 3.
There are many scenarios that satisfy statement 1. Here are two:
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The value of M is 7.
There are many scenarios that satisfy statement 2. Here are two:
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the target question is L = 4
Case b: J = 1, K = 3, L = 5, M = 7, N = 8. In this case, the answer to the target question is L = 5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent­

What if we apply Mean concept here. As 5 variables are in the ascending order. The Value of L can be identified by knowing K and M.

L = (K+M)/2

TheFlash

I thought that too. But then values are in ascending order and not equidistant (AP).

There is a difference between 1,6,7,9,10 and 1,2,3,4,5.

Following me?

(A) Just knowing the value of \(K\) tells us that \(L>3\) but we cannot determine a unique value for \(L\).

(B) Just knowing the value of \(M\) tells us that \(L<7\) but we cannot determine a unique value for \(L\).

Combining the two we get
\(3<L<7\) but we still cannot determine a unique value for \(L\) as \(L\) could be \(4\) or \(5\) or \(6\).

Hence, E.­